1 Introduction

A supply chain is a network of various entities such as suppliers, manufacturers, wholesalers, retailers, who coordinate with each other, to make, and sell a product or service. Collaboration with suppliers at low operational risk can possibly reduce the chances of losses or disruptions among the entities. The supplier acts as a starting point for any supply chain. Therefore, it becomes important for any supply chain to consciously make supplier selection as it is one of the key activities required for implementing a robust supply chain management (Claudia et al. 2016; Mohammed et al. 2018; Verdecho et al. 2020; Fallahpour et al. 2021; Rezaei et al. 2021). Its main aim is to identify the best suppliers and undertake resource allocation decisions for procurement of goods from them.

Moreover, procurement function is considered as one of the key function for companies because the costs associated with it accounts for more than 50% of all internal costs (Yazdani et al. 2016). Also, the supplier selection can be either single sourcing or dual (multiple) sourcing. In single sourcing, organisations rely on one supplier to fulfil their demand, and decision-maker has to decide about the superior supplier. In dual or multi-sourcing, as single supplier cannot fulfil all the company’s demands, multiple suppliers need to be selected. Thus, supplier selection problem is a multifaceted, multi-criteria decision-making activity since different and conflicting criterions are required to be considered and assessed for selection of suppliers (Luthra et al. 2017; Taherdoost and Brard 2019; Aouadni et al. 2019a, b; Chan and Kumar 2007; Dickson 1966).

Traditionally, supplier selection is based on the ability of the supplier to meet the quality requirements, on-time deliveries, and pricing strategies. However, today the selection has become challenging because organizations today select sustainable suppliers who consider economic, green, and social aspects (Azadeh et al. 2017; Saroha et al. 2021). In principle, organisations carry the supplier assessment based on various criterions. The supplier evaluation and assessment process has changed remarkably in past few years with the use of information technology and computers. The literature review reveals that various methodologies have been used for supplier selection and evaluation such as multi criteria decision-making methods (MCDM), mathematical programming and artificial intelligence techniques (Aouadni et al. 2019a, b). Several multi-criteria methods have been adopted by the researchers for supplier selection (Muralidharan et al. 2002; Shyur and Shih 2006; Omurca, 2013; You et al. 2015; Yazdani et al. 2016; Luthra et al. 2017; Mohammed et al. 2018; Kannusamy, and Thangavelu 2019; Fallahpour et al. 2021). The mathematical models are applications of linear programming, binary integer linear programming, mixed-integer nonlinear programming, dynamic programming, stochastic programming and other quantitative approaches (Che and Wang 2008; Choudhary and Shankar 2013; Guoand Li 2014; Adeinat and Ventura 2015; Pazhaniet al. 2016; Ghaniabadi and Mazinani 2017; Govindan et al. 2020). Owing to their complexity, the application of mathematical models has not received much attention in service industries and other sectors. On the other hand, MCDM methods are easy to use, and their success depends upon human judgement (Aouadni et al. 2019a, b). According to Jain et al. (2018) and Agrawal and Kant (2020) fuzzy based approaches could be effective and handle the element of uncertainty or subjective judgements more accurately than the existing approaches used to address supplier selection problems.

In literature, researchers have made substantial efforts to develop various frameworks/ models for selecting the suppliers based on different criterions (Srinivasan et al. 2011; Luthra et al.2017; Taherdoost and Brard 2019; Fallahpour et al. 2021; Rezaei et al. 2021). However still, there is a need to develop a sound supplier selection and assessment model. Such a model is supposed to be based upon various dimensions critical to supplier section. Further, these dimensions are required to be checked for structural dependences among them so that managers can understand the existence of complex relationships between them. Before proposing any framework or model, it is essential to realize the importance of each dimension and its role in the supplier selection process. It is also required to examine the importance and relationships of dimensions among themselves. To this effect the present study aims to identify, analyze and model various dimensions which may affect the supplier selection process. The study uses ISM based methodology for understanding the interactions among various dimensions followed by driver-dependence power analysis.

The major contributions of this work are:

  • Identification of the various dimensions related to supplier selection in an outsourcing environment

  • Modelling the association among the dimensions and to identify potential driver dimensions

  • To build a fuzzy-based inference system that helps to analyze the effect of driver dimensions on the supplier selection.

2 Literature review

Table 1 summarises the work done by various researchers on supplier selection issues.

Table 1 Summary of literature studies
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3 Research questions and methodology

The main research questions addressed in this work are:

  • RQ1 What are the various dimensions associated with supplier selection in outsourcing environment?

  • RQ2 How these dimensions structurally interact with each other?

  • RQ3 What is the degree of dependence among various dimensions which affect supplier selection decisions in outsourcing environment?

  • RQ4 How the key dependent dimensions can be modelled to address the uncertainties associated with supplier selection problem?

The above-stated questions are answered by developing a research framework (Fig. 1) consisting of two phases. In the first phase, various dimensions associated with supplier selection in an outsourcing environment have been identified with the help of careful examination of literature and discussion with experts. ISM method is then used to model the structural association among these dimensions. The justification for use of ISM method to prioritize and analyze the association among supplier dimensions is based on its comparison with contemporary modelling techniques i.e. ANP and AHP as shown in the Table 2 (Thakkar et al. 2008). Owing to the exceptional features of ISM over AHP and ANP, authors preferred to use the ISM approach in their work. Also, in literature, the application of the ISM approach has been found to address multifaceted engineering problems, supply chain and vendor management problems, software project activities (Pfohl 2011; Rane and Kirkire, 2017; Sindhwani and Malhotra 2017; Kumar et al. 2019; Biswal et al. 2019; Sharma and Sangal 2019, Wankhade, and Kundu, 2020; Hughes et al. 2020). In the second phase, MICMAC analysis is carried out to study the effect of dimensions by developing the hierarchies based on driver and dependence power. It portrays dimensions under various clusters i.e. dependent, independent, linkage, and autonomous. Lastly, an inference system based on fuzzy logic has been built to examine the influence of dependent dimensions on supplier selection.

Fig. 1
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Research framework

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Table 2 Comparison among research methods
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3.1 Supplier selection dimensions

After critical scrutiny of literature studies as discussed in Table 1, the following dimensions have been identified for supplier selection in an outsourcing environment.

  1. 1.

    Quality: It is stated as the ability of supplier to meet quality specifications constantly. It includes sub-dimensions related to accuracy, reliability, performance etc.

  2. 2.

    Delivery rate/ Service: It is defined as the ability of the supplier to adhere delivery timelines.

  3. 3.

    Production capacity: It is related to suppliers' infrastructure related to production facility, its capacity, and overall exploitation.

  4. 4.

    Price: It is defined as net price of the product after discounts.

  5. 5.

    Economical Environment: It shows the supplier’s financial health in terms of liquidity ratio, solvency position, and credit rating policy.

  6. 6.

    Technological level: It is defined as presence of adequate manpower and the state of technological know-how.

  7. 7.

    Management and organization: It refers to the supplier’s management, its organization to coordinate and utilize resources effectively and efficiently to meet organisational goals.

  8. 8.

    Transportation and communications: It is related to geographical location of the supplier and the presence of communication channels.

  9. 9.

    Trust: Supplier trust is the purchaser's trust in the supplier's ability to accomplish the task.

  10. 10.

    Labour relations: It refers to the nature of labour relations and conflict management practises in the company

  11. 11.

    Agility: It is the ability of an organization to respond to change and rapidly adapt to market and environmental changes in useful and cost-effective manner.

  12. 12.

    Risk management: It means reducing vulnerability and ensuring continuity in supplies.

3.2 Model development

ISM approach is based on utilizing domain expert’s knowledge to disintegrate a complex system into numerous subsystems and build a hierarchal system model that portrays inter-relationships among subsystems. The method involves the following steps:

  1. 1.

    Listing of factors/dimensions which may affect the system.

  2. 2.

    Assigning the contextual association among the factors/dimensions listed out in the first step. Following terminology is used for developing the contextual relationship.

    1. a.

      V: it is used to denote the influence of dimension i on dimension j.

    2. b.

      A: it is used to denote the influence of dimension j on dimension i

    3. c.

      X: it is used to denote the influence when i and j will lead to each other

    4. d.

      O: it is used to denote when dimension i and j will not lead to each other

  3. 3.

    Development of structural self-interaction matrix (SSIM) for factors/dimensions, to demonstrate pair wise association between them.

  4. 4.

    Development of Reachability matrix from the SSIM matrix and examining it for transitivity, which is further, partitioned into different levels, as iterations proceeds.

  5. 5.

    Making di-graph and eliminating the transitive links among dimensions.

  6. 6.

    Developing the ISM model from the digraph and replacement of nodes with words.

3.2.1 Structural self interaction matrix (SSIM)

A contextual relationship of "leads to" type is chosen for analyzing the dimensions for supplier selection in an outsourcing environment. This means that one dimension helps to improve another dimension. It is on this premise; a contextual association among the dimensions is established. The terminology discussed in step 2 above is used to develop the contextual association between the supplier selection dimensions (i & j). The details of the SSIM matrix are presented in Table 3.

Table 3 Matrix representing contextual association
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3.2.2 Reachability matrix

The matrix representing contextual association is converted into a 0–1 matrix called the reachability matrix obtained by substituting V, A, X, O with either 0 or 1. Afterward it is checked for transitivity.

Rules for obtaining reachability matrix.

  • If (i, j) is written as V in the self-interaction matrix, then in the reachability matrix (i, j) entry becomes 1, and the (j, i) entry are made 0.

  • If (i, j) is written as A in the self-interaction matrix, then in the reachability matrix the (i, j) entry becomes 0, and the (j, i) entry are made 1.

  • If (i, j) is written as X in the self-interaction matrix then in the reachability matrix both the (i, j) and (j, i) entries are made 1.

  • If (i, j) is written as O in the self-interaction matrix, then in the reachability matrix both the (i, j) and (j, i) entries are made 0.

Thus, the final reachability matrix is refined using the transitivity rule, which is stated as if "A" is linked to "B" and "B" is linked to "C", then as a consequence, "A" is linked to "C”.

Following these rules, the reachability matrix is obtained, as shown in Table 4.

Table 4 Reachability matrix
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The transitive elements in the final reachability matrix are shown by 1*.After including the transitivity links, we obtained the final reachability matrix (Table 5).

Table 5 Final reachability matrix
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3.2.3 Level partition

Once the reachability matrix is formed, two sets i.e. reachability and antecedent sets are obtained. The reachability set contains dimension i and other dimensions which drive or influence it. Similarly, the antecedent set contains dimension i and other dimensions which drive or influence it. Subsequently, the intersection set is obtained which contains common dimensions of both reachability and antecedent sets. Those dimensions in which reachability and intersection set are similar, they are given the highest precedence relationship in the structural model, and consequently that dimension is detached from the remaining sets. The procedure of awarding precedence relationship is continued until all the levels are ascertained. It took five iterations to complete the process in the present case, as presented in Table 6.

Table 6 Iterations
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3.2.3.1 Lower triangular matrix

A lower triangular matrix is obtained by arranging the various dimensions at the similar level across rows and columns of the final reachability matrix. Table 7 presents the lower triangular matrix.

Table 7 Lower triangular matrix
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3.2.4 Formation of diagraph and ISM

Dimensions in the diagraph are placed according to the levels obtained during the iterations. As shown in Table 6, for the problem, it took a total of five iterations to complete the process.

The dimensions found in the iteration-I are placed at the uppermost position in the hierarchy and the dimensions found in the iteration-II are placed at the subsequent level and the procedure is repeated until all the dimensions so obtained in different iterations are positioned in the hierarchal model. Figure 2 presents the ISM for supplier selection with five levels.

Fig. 2
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Interpretive structural models for supplier selection

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4 Phase-II MICMAC analysis and fuzzy logic

4.1 MICMAC analysis

To answer RQ3 i.e., the influencing dynamics of various supplier selection dimensions in outsourcing environment MICMAC (cross-impact matrix multiplication applied to classification) analysis has been performed. The method is based on the multiplication properties of matrices (Mandal and Deshmukh 1994) and divides the various dimensions into four categories as dependent, independent, influential, and autonomous dimensions (Biswal et al. 2019; Wankhade and Kundu 2020).

The dependence and the driving powers of all the supplier dimensions considered in the study are presented in Table 5 Sect. 3.2.2. From the table, it is observed that rows with entries of ‘1’ are used to indicate the driving power and column entries are used to indicate the dependence power of the dimensions. Using this information, the MICMAC matrix diagram is made, as depicted by Fig. 3. As an illustration, it can be inferred from Table 5 that dimension number 7 i.e. management and organization has a score of 10 under driving power of 10 and has a score of 1 under dependence power. Hence, based on the scores the dimension 7 is placed in quadrant 4 represented by independent category in the MICMAC diagram.

Fig. 3
figure 3

Driving power and dependence diagram

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Further, all the supplier selection dimensions are grouped under four clusters.

  • Cluster 1: In the study, no dimension figures out in the autonomous cluster, which indicates that all dimensions are important and has to be considered by the management for supplier selection in an outsourcing environment.

  • Cluster II: The three dimensions i.e. Quality, Service, and Cost dimensions fall in the dependent category. As evident from Fig. 3 these dimensions possess the least driving power and high dependence power. These are placed at the uppermost position i.e. at level1 in the ISM model.

  • Cluster III: In this cluster five dimensions i.e. production facilities & capacity, trust, agility, technical capability and risk management are placed. These dimensions are called linkage dimensions as they are affected by dimensions at lower-level and as a result, they impact the left over dimensions in the hierarchical model.

  • Cluster IV: The dimensions like economic environment, labour relations, transportation, and management and organisation are grouped in this cluster and they are called independent dimensions.

4.2 Fuzzy logic

To answer RQ4 an inference system based on fuzzy logic has been build. The basic structure of the proposed system is presented in Fig. 4.

Fig. 4
figure 4

Fuzzy inference system

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The key components of the system are.

  • Fuzzification: This process in fuzzy system is used to relate the numerical value of the input dimensions to the values on the linguistic scale.

  • Fuzzy (If–Then) rules: After completing fuzzification, if–then rules are generated. These rules express and model the domain expert’s knowledge in if–then format. The rule base is formed by obtaining knowledge collected from professional experts, databanks, and previous literature on the subject (Xie et al. 1999, Ross 2009). For instance, fuzzy rule is composed as: If M is Ai, THEN N is Bi

  • Fuzzy inference system: Being a main unit of fuzzy logic system it is used to interpret the values in the input vector and, on the basis of some sets of rules, it assigns the values to the output vector. Two most common types of inference systems widely used are: Mamdani-type and Sugeno-type.

  • Defuzzification: It is defined as the process of converting a fuzzy number into a precise or single value. Various forms of defuzzification methods are available in literature such as center of gravity (COG), mean of maximum (MOM), and center average methods (Ross 2009).

4.2.1 Illustrative case

The notion of fuzzy logic application in the selection of prospective suppliers is discussed with the help of case study approach by considering textile, textile product, and apparel manufacturing industries. The supply chains in these industries are so intricate that it has become challenging to cope with supplier relationships effectively. Thus, selecting the genuine supplier from the very beginning is important in order to ensure that deliveries are made on right time, with right quality and desired quantity. To this effect, various dimensions are used when potential suppliers are to be evaluated. In literature, various authors paid attention to cost, quality, and service dimensions (Ghodsypour and O’Brien 1998; Braglia and Petroni 2000; Kumar et al. 2013; Kumar and Pani 2014; Taherdoost and Brard 2019; Fallahpour et al. 2021; Rezaei et al. 2021). In the study, the three dimensions, i.e., quality, service, and cost were considered as inputs to address the supplier selection problem. In business strategies, the sub-dimensions for quality include low defect rates and high process capability, similarly for service the sub-dimensions are on-time deliveries, quickness to respond to changes and flexible processes. For cost, various sub-dimensions are cost related to inland transportation, cost and freight price, tariff and taxes, warehouse storage etc. (Ghodsypour and Brien 1998; Sharon Ordoobadi 2009; Li and Zeng 2016). A questionnaire (shown in appendix) is designed to collect the data from the key stakeholders in textile, textile product, and apparel industries by considering the above dimensions.

The following paragraphs present the details of the proposed method.

Linguistic terms The terms low, medium, and high are used as linguistic terms to define the input dimensions, i.e., quality, cost, and time, used in the study for supplier selection.

Fuzzification In the study, the input variables are fuzzified using trapezoidal membership functions, and output membership functions for three suppliers (X, Y&Z) are fuzzified using the triangular membership function. Figure 5 presents the membership functions for inputs i.e. cost, quality, and service. Figure 6 presents output membership function plots for three suppliers (X, Y&Z). For the cost dimension, range of input is 70–100. According to Ghodsypour and O’Brien (2001), on an average in product cost the purchased materials and services represent up to 70%. For the firms dealing with high technology, the product cost for purchased materials and services constitute up to 80%. For the dimension quality, the defect rate is used to define the membership function, which ranges from 0.01 to 0.09. The range of other sub-dimension i.e. ‘service level’’ the range considered is between 0.4–1. The decision maker can decide any value. Three options considered in the study are: Good (0.40–0.55), better (0.50–0.85), and Best (0.8–1).

Fig. 5
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Input membership functions for cost, quality, and service

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Fig. 6
figure 6

Output membership functions for Supplier A, Supplier B, and Supplier C

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Rule base and Fuzzy inference system Based on the alternate combinations of input dimensions, the rule base is developed in this step to provide a computational mechanism in if–then form. According to Jin (2000), a fuzzy inference system may consist of numerous rules as possible in order to fill the input–output domain of the system. Conversely, it shall consist of limited number of rules because large set of rules bounds the generalization of the model. In the study, based upon the input dimensions and linguistic terms used to represent these dimensions, a total of 27 rules have been made. Figure 7 shows the rules generated in the FIS editor for the supplier selection problem.

Fig. 7
figure 7

Rules framed in the rule base editor

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Developed by Wang and Mende1 (1992), the inference system maps the situation –action pairs using a given set of inputs and outputs. In the study, Mamdani’s method is used to map the inputs with outputs. The max–min operator used in Mamdani system is presented in Eq. (1)

$$\mu_{B} (y) = \min - \max (\beta_{k} ,\mu_{{B_{k} }} (y)),$$
(1)

where, βk = min αi,k [αi,k = sup min (μA′ (xi). μAi,k (x)].

Graphically, Eq. 1 is depicted in Fig. 8. The symbols R11 and R12 signify fuzzy antecedents of Rule 1, and the symbol B1 signifies consequent part of Rule 1. “And” connector is used to link the antecedent pairs in rules. The fuzzy inference process is carried out for two rules as shown in Fig. 8 respectively.

Fig. 8
figure 8

Mamdani fuzzy inference process

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The aggregated fuzzy set is obtained by using the centroid method for defuzzification. It is represented as shown by Eq. (2).

$$y = \smallint {\text{y}}\mu {\text{Aggr}}\left( {\text{y}} \right){\text{dy}}/\smallint \mu {\text{Aggr}}\left( {\text{y}} \right){\text{dy}}$$
(2)

where; μAggr(y) represents the fuzzy set obtained after aggregation and the denominator ∫μAggr(y) represents the area below μAggr(y).

5 Results and discussions

As discussed in the beginning of Sect. 4.2.1, to illustrate the concept of fuzzy logic in selecting prospective suppliers, we considered textile, textile product, and apparel manufacturing industries. Data with respect to sub dimensions representing the quality, service and cost dimensions is collected from the respondents who were mainly the managers responsible for looking procurement, production, and quality control functions in their organisations. The sample questionnaire is presented in the “Appendix” which is used to get the responses. Questionnaire results were summarised, which were mainly based on the qualitative assessment on five point scale (least important-highly important). Additionally, the experience, and perception of experts on cost, quality and service dimensions forms the basis for conducting simulations under various settings.

In the first simulation experiment, the cost is considered high, quality is considered low, and service is considered high. With respect to these three input combinations, the simulation output for three suppliers so obtained are 0.502 (supplier X), 0.498 (supplier Y) and 0.583 (Supplier Z); which shows that supplier Z performs better and hence is recommended under the stated linguistic input dimensions used to select the supplier.

In the second simulation experiment the cost is considered as moderate, quality is considered as moderate, and service is considered as high. with respect to these three input combinations the simulation output for three suppliers so obtained are 0.54 (supplier X), 0.460 (supplier Y) and 0.444 (Supplier Z); which shows that supplier X performs better and hence is recommended under the stated linguistic input dimensions used to select the supplier.

In the third simulation experiment the cost is considered as high, quality is considered as low, and service is considered as moderate. With respect to these three input combinations the simulation output for three suppliers so obtained are 0.478 (supplier X), 0.522 (supplier Y) and 0.504 (Supplier Z); which shows that supplier Y performs better and is recommended under the stated linguistic input dimensions used to select the supplier.

Similar experiments can be conducted with different linguistic settings of input dimensions related to cost, quality, and service and supplier selection process based upon organizational needs can be achieved.

Table 8 presents the results of simulation experiments with input dimensions related to cost, quality and service. The values of scores obtained for Supplier X, Y and Z are also shown with final recommendation. Figure 9a–c shows the simulation outputs. Similar studies for supplier selection problem under fuzzy environment were conducted in literature by Kumar et al. (2013); Azadeh et al. (2017); Eydi and Fazli, (2019); Fallahpour et al. (2021) which signifies the importance of the present study. Thus, the approach presented in the study provides a decision making framework which enables the managers to assess the supplier performance based on key dimensions.

Table 8 Simulation experiments with input parameters and results
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Fig. 9
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a–c Simulation results

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6 Conclusions and future scope

The present work provides a hybrid approach to support supply chain professionals in undertaking decisions related to identification of the key dimensions involved in supplier selection. Based upon the critical scrutiny of literature studies eleven important dimensions related to the supplier selection problem are ascertained. To define the structural relationship between these dimensions, ISM model is developed. The model portrays these dimensions at various levels. At level 1 dimension management and organization is there followed by three dimensions i.e. economic environment, labor relations and transportation and communications at Level II. All these dimensions come under independent category, which means that they possess strong dependence and least driving power. Level III comprises of five dimensions i.e., production capacity, agility, trust, technological level and risk management. These are called linkage dimensions as both driving power and dependence power are strong. Level IV consists of one dimension only i.e. quality and Level V has two dimensions i.e. delivery rate/service and cost. They figure at top of the ISM model.

In addition, a case study based on qualitative analysis has been developed by considering three prospective suppliers from textile, textile product, and apparel manufacturing industries. Data is collected from these companies on quality, service and cost dimensions on the five-point scale. Further, by developing an inference system based on fuzzy logic, the simulation experiments were conducted with different combinations of three dependent dimensions i.e., cost, quality, service and delivery to show that the supplier selection process may vary with the organization’s needs. The results presented in Sect. 5 indicate the most appropriate supplier under different settings. For instance, when the cost is considered high, quality is considered low, and service is considered high than supplier Z performs better and hence is recommended.

The novel approach proposed in the study is very flexible and can be adopted by managers to address the real supplier selection issues. In literature too Azadeh et al. (2017) in their study measured the effects of dimensions i.e. customer trust, cost, and delivery time simultaneously for selecting the most appropriate supplier in an auto parts manufacturer to control potential SCM disruptions. They used fuzzy data envelopment analysis to handle the problem of data subjectivity and uncertainty. Thus, present study successfully demonstrates the applicability of proposed approach for supplier selection problem. For future work more dimensions that measure supplier performance could be included in the analysis. In addition to this, future researchers should also focus on supplier development dimensions figured in quadrant IV of the driver–dependence diagram. Other modelling techniques such as analytical hierarchy process, fuzzy ISM/MICMAC, or structural equation modelling can be explored, and the results could be validated. Taking into account the inherent complexities involved in the supplier selection the future researchers can use risk aversion tools (failure mode effects analysis (FMEA); hazard and operability study (HAZOP), fault tree analysis (FTA) etc.) which can help the organizations to strengthen their supply chains and mitigate the possible risks in supplier selection process. Table 9 summarizes the research questions with discussions.

Table 9 Summary of research questions
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